Ensembles, Dynamics and Cell Types

The human genome encodes 23,000 proteins and perhaps more functional RNA sequences. Some vast genetic regulatory network couples these genes controlling their dynamical behaviors. Might the generic behaviors of some ensemble of dynamical systems predict aspects of ontogeny? Yes: Random Boolean Networks, RBN. Such anetwork has N binary variables, each with K inputs randomly chosen among the N, and governed by a randomly chosen Boolean function of K inputs. Time is discrete. The variables update synchronously. Any choice of N and K generates an ensemble.
A system’s state follows a trajectory in state space that flows to one repetitive cycle of states, an attractor. A network may have many attractors.
Such networks can be “Ordered”, “Critical” or “Chaotic”. K <2.0 is ordered. K =2.0 is critical. K > 2.0 is chaotic. Biases in the Boolean functions yield another parameter, P. In the K P plane a line of criticality separates order from chaos.
Critical networks are of high interest. The length of state cycles scales as square root N, the number of attractors scales as square root N, intense localization.
The natural hypothesis is that a cell type corresponds to an attractor of the network. Good evidence supports this.
The theory that evolved genetic regulatory networks are generic members of the critical ensemble predicts that the number of cell types in an organism should scale as a power law with respect to DNA per cell. The data across 11 distinct phyla shows a power law scaling of 0.88.
Cells appear dynamically critical, with a power law distribution of alteration in gene expression upon single mutations, and parallel flow in state space on perturbations.
Selection on chaotic or ordered networks yields critical networks suggesting an evolutionary pathway to their emergence.
Ensemble Theories bear on biology beyond Natural Selection.
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